Roadmap — Math-Based Programming Fundamentals (150 problem)¶

এটা পুরো math section-এর master map — 12টা level, 150টা problem, একটা সাজানো ক্রম। নিয়ম সহজ: ID ধরে এগোও (001 → 150)। ক্রমটা ইচ্ছে করে easy → hard, আর প্রতিটা problem আগের কোনো problem-এর idea-র উপর দাঁড়ানো — তাই লাফ দিলে পরেরটা ঝুলে যায়। Difficulty: Easy = গতি-আত্মবিশ্বাস, Medium = মূল শেখা, Hard = চ্যালেঞ্জ (CP-deep)। বিস্তারিত (concept, ছবি, "Inherits from" chain, full tracker) প্রতিটা level-এর folder-এ; এখানে শুধু এক নজরে।

Level 0 — Absolute Basics¶

#	Problem	Difficulty
001	Even or Odd	Easy
002	Sum of Digits	Easy
003	Count Digits	Easy
004	Reverse Number	Easy
005	Palindrome Number	Easy
006	Armstrong Number	Easy
007	Digital Root	Easy
008	Find Last Digit	Easy
009	Power of 10 Check	Easy
010	Number Pattern Printing	Easy

Level 1 — Divisibility, Prime, GCD, LCM¶

#	Problem	Difficulty
011	Divisibility Rules	Easy
012	Count Factors	Easy
013	Check Prime	Easy
014	Print All Primes up to N	Easy
015	Sieve of Eratosthenes	Medium
016	Prime Factorization	Medium
017	Smallest Prime Factor	Medium
018	GCD using Euclidean Algorithm	Easy
019	Extended GCD Intro	Hard
020	LCM using GCD	Easy
021	Coprime Check	Easy
022	Count Coprime Pairs Basic	Medium
023	Euler Phi Basic	Medium
024	Number of Divisors	Medium
025	Sum of Divisors	Medium

Level 2 — Modular Arithmetic¶

#	Problem	Difficulty
026	Remainder Basics	Easy
027	Modular Addition	Easy
028	Modular Multiplication	Easy
029	Modular Exponentiation	Medium
030	Fast Power	Medium
031	Large Number Mod	Medium
032	Modular Inverse Basic	Medium
033	Fermat Little Theorem	Medium
034	nCr mod Prime	Hard
035	Modular Division	Medium
036	Cyclic Remainder Pattern	Easy
037	Clock Arithmetic Problems	Easy
038	Hashing with Mod	Medium

Level 3 — Counting & Combinatorics¶

#	Problem	Difficulty
039	Factorial	Easy
040	Permutation Basic	Easy
041	Combination Basic	Easy
042	nCr using Pascal Triangle	Medium
043	Stars and Bars Basic	Medium
044	Inclusion-Exclusion Basic	Medium
045	Count Pairs	Easy
046	Count Triplets	Medium
047	Count Subsets	Easy
048	Count Paths in Grid	Medium
049	Catalan Number Intro	Medium
050	Derangement Intro	Medium
051	Pigeonhole Principle Problems	Medium
052	Birthday Paradox Style Problems	Medium

Level 4 — Bit Manipulation¶

#	Problem	Difficulty
053	Binary Representation	Easy
054	Check ith Bit	Easy
055	Set ith Bit	Easy
056	Clear ith Bit	Easy
057	Toggle ith Bit	Easy
058	Count Set Bits	Easy
059	Power of Two	Easy
060	Odd One Out using XOR	Easy
061	Find Two Unique Numbers	Medium
062	Subset Generation using Bits	Medium
063	Bitmask DP Intro	Hard
064	Gray Code	Medium
065	AND/OR/XOR Range Tricks	Medium
066	Maximum XOR Pair	Hard

Level 5 — Prefix, Difference, Contribution¶

#	Problem	Difficulty
067	Prefix Sum	Easy
068	Range Sum Query	Easy
069	Difference Array	Medium
070	Range Update Query	Medium
071	Prefix XOR	Medium
072	2D Prefix Sum	Medium
073	Subarray Sum Equals K	Medium
074	Count Subarrays Divisible by K	Medium
075	Contribution Technique Basic	Medium
076	Sum of All Subarrays	Medium
077	Sum of Subarray Minimums	Hard
078	Pair Contribution Problems	Medium
079	Imos Method Basic	Medium
080	Sweep Line Intro	Medium

Level 6 — Two Pointers & Sliding Window Math¶

#	Problem	Difficulty
081	Two Sum Sorted	Easy
082	Pair with Difference K	Medium
083	Three Sum	Medium
084	Container With Most Water	Medium
085	Sliding Window Sum	Easy
086	Longest Subarray with Sum K (Positive)	Medium
087	Minimum Size Subarray Sum	Medium
088	Count Subarrays with At Most K Distinct	Medium
089	Count Subarrays with Exactly K Distinct	Hard
090	Number of Subarrays with Product Less Than K	Medium

Level 7 — Binary Search on Answer¶

#	Problem	Difficulty
091	Basic Binary Search	Easy
092	Lower Bound	Easy
093	Upper Bound	Easy
094	Search Insert Position	Easy
095	Square Root using Binary Search	Easy
096	Minimum Eating Speed	Medium
097	Ship Packages Within D Days	Medium
098	Aggressive Cows	Medium
099	Allocate Minimum Pages	Medium
100	Split Array Largest Sum	Hard
101	Median of Two Sorted Arrays	Hard
102	Kth Smallest in Multiplication Table	Hard

Level 8 — Greedy Math Tricks¶

#	Problem	Difficulty
103	Minimum Coins Basic	Easy
104	Jump Game	Medium
105	Gas Station	Medium
106	Candy Distribution	Hard
107	Interval Scheduling	Medium
108	Minimum Platforms	Medium
109	Rearrange with Constraints	Medium
110	Maximum Product by Splitting	Medium
111	Make Array Equal with Minimum Moves	Medium
112	Minimize Maximum Difference	Medium

Level 9 — Geometry & Coordinate Math (CP-optional)¶

#	Problem	Difficulty
113	Distance Between Points	Easy
114	Slope and Collinearity	Easy
115	Area of Triangle	Easy
116	Orientation of Three Points	Medium
117	Line Intersection Basic	Medium
118	Rectangle Overlap	Medium
119	Circle and Point	Easy
120	Convex Hull Intro	Hard
121	Manhattan Distance Tricks	Medium
122	Rotate Matrix and Coordinates	Medium
123	Grid Movement Math	Medium
124	Pick's Theorem Intro	Hard

Level 10 — Advanced Number Theory (CP-optional)¶

#	Problem	Difficulty
125	Extended Euclidean Algorithm	Medium
126	Linear Diophantine Equation	Medium
127	Chinese Remainder Theorem Basic	Hard
128	Euler Totient Advanced	Medium
129	Mobius Function Intro	Hard
130	Modular Inverse Advanced	Medium
131	Matrix Exponentiation	Hard
132	Fibonacci using Matrix Exponentiation	Hard
133	Fast Doubling Fibonacci	Hard
134	Primality Test Advanced	Medium
135	Miller-Rabin Intro	Hard
136	Pollard Rho Intro	Hard
137	Sieve Variants	Medium
138	Segmented Sieve	Hard

Level 11 — Hard Mixed CP Patterns (CP-optional)¶

#	Problem	Difficulty
139	Meet in the Middle	Hard
140	Ternary Search	Medium
141	Game Theory Basics	Medium
142	Nim Game	Medium
143	Grundy Number Intro	Hard
144	Expected Value Problems	Medium
145	Probability DP	Hard
146	Burnside Lemma Intro	Hard
147	Matrix Power on Graphs	Hard
148	Inclusion-Exclusion Hard	Hard
149	Combinatorics with DP	Hard
150	Constructive Math Problems	Hard

কোথা থেকে শুরু করবে¶

basics-এ মরচে পড়ে গেছে, হাতে দিনে 2-3 ঘণ্টা — তাহলে পরিকল্পনাটা এমন:

শুরু করো Level 0 (Absolute Basics) থেকে। সহজ লাগলেও skip কোরো না — গতি আর নির্ভুলতা এখানেই তৈরি হয়।
দিনে 1-2টা problem। আগে নিজে অন্তত 20-30 মিনিট চেষ্টা, তারপর note/concept মেলানো। গোনার চেয়ে গাঁথা জরুরি।
সপ্তাহে একদিন revision — আগের 6-8টা problem আবার চোখ বুলিয়ে, একটা dry run হাতে করে দেখা।
Level 00-08 আগে শেষ করো (interview-critical)। তারপর মূল data structures (02-13); Level 09-11 (CP-optional) পরে — DP শেখার পরে level 11-এর অর্ধেক এমনিই সহজ। আটকে গেলে আগের level-এর concept-notes আর "Inherits from" chain-এ ফেরো — উত্তরের সূত্র প্রায়ই সেখানেই।

ধৈর্য রাখো — 150টা problem এক দৌড়ে নয়, এক একটা ধাপে। প্রতিটা টিক-মার্ক একটা ছোট জয়। শুভকামনা!